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• W2891259554 abstract "Denote by $T$ the transformation $T(x)= 2 ,x $ (mod 1). Given a potential$A:S^1 to mathbb{R}$ the main interest in Ergodic areprobabilities $mu$ which maximize $int A ,d mu$ (among invariantprobabilities) and also calibrated subactions $u: S^1 to mathbb{R}$. We willanalyze the $1/2$-operator $mathcal{G}$ which acts on Holder functions $f:S^1 to mathbb{R}$. Assuming that the subaction for the Holder potential $A$is unique (up to adding constants) it follows from the work of W. Dotson, H.Senter and S. Ishikawa that $lim_{n to infty} mathcal{G}^n (f_0)=u$ (forany given $f_0$). $mathcal{G}$ is not a strong contraction and we analyze herethe performance of the algorithm from two points of view: the generic point ofview and its action close by the fixed point. In a companion paper (Explicit examples in Ergodic Optimization) we willconsider several examples. The sharp numerical evidence obtained from thealgorithm permits to guess explicit expressions for the subaction: among themfor $A(x) = sin^2 ( 2 pi x)$ and $A(x) = sin ( 2 pi x)$. There we present apiecewise analytical expression for the calibrated subaction in this case. Thealgorithm can also be applied to the estimation of the joint spectral radius ofmatrices. Explicit examples in Ergodic Optimization is on the sitehttp://mat.ufrgs.br/~alopes/examp-1-2-13jun2018.pdf" @default.
• W2891259554 created "2018-09-27" @default.
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• W2891259554 date "2018-09-03" @default.
• W2891259554 modified "2023-09-27" @default.
• W2891259554 title "An algorithm for approximating subactions" @default.
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• W2891259554 hasPublicationYear "2018" @default.
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